Validation and personality conditionings of the 3 × 2 achievement goal model in sport

Achievement goal models have been successfully applied in sport. In recent years, a framework that has emerged in this area is the 3 × 2 approach, being a natural evolution of years of research into the issue of achievement goals. Nevertheless, it is essential to further validate the abovementioned approach and explore its psychosocial context. Hence, the purpose of this study was to validate the latest 3 × 2 achievement goal model among high-performance and recreational athletes using the Polish version of the 3 × 2 Achievement Goal Questionnaire for Sport (3 × 2 AGQ-S), and to determine the relationship between personality traits and achievement goals of athletes. The study included 413 athletes, with M = 20.62 and SD = 2.72. The 3 × 2 AGQ-S was used to assess achievement goals, the Big Five personality traits were assessed using the IPIP-BFM-20 questionnaire. The model of the Polish version of the 3 × 2 AGQ-S achieved a satisfactory fit to the data (CFI = 0.940, TLI = 0.923, RMSEA = 0.086, SRMR = 0.061). Cronbach’s alphas for the subscales were: 0.77–0.96. High-performance athletes obtained higher achievement goals in task and self subscales than recreational athletes. Personality traits explained no more than 3% of variance of achievement goals in sport. Research involving the Polish version of the 3 × 2 AGQ-S supports the validity of the 3 × 2 model in sport among high-performance and recreational athletes. Nevertheless, the small relationships between the personality traits and achievement goals prompt searching for other psychosocial determinants of goals in sport.


Instruments
The 3 × 2 Achievement Goal Questionnaire for Sport (3 × 2 AGQ-S) by Mascret et al. 8 was used to test goal achievements.The questionnaire consisted of 18 statements, and the respondents' task was to rate on a scale from 1 to 7 how much each statement applied to them.The questionnaire contained 6 subscales (3 statements for each), i.e., task-approach, task-avoidance, self-approach, self-avoidance, other-approach, other-avoidance.First, a language expert translated the scale into Polish.Then another language expert back-translated the scale into English.A group of experts consisting of three sport psychologists and a translator established the final Polish version of the scale.At the outset, the subjects were asked to raise any doubts they had about their understanding of the statements.Yet, no doubts were raised.
The IPIP-BFM-20 questionnaire was used to determine the personality traits from the Big Five model.It consisted of 20 test items, with four test items for each of the five personality traits (emotional stability: α = 0.76, extraversion: α = 0.83, agreeableness: α = 0.68, conscientiousness: α = 0.73, intellect: α = 0.70).The respondents' task was to assess how much each statement applies to them on a 1-5 scale 35 .

Procedure
The participants were first informed that their participation in the study was voluntary and that they could withdraw from the study at any time.They were also asked if they had any health contraindications, physical and mental state conditions at the time of the study, or any other obstacles that would hinder their participation or prevent them from taking part in the study.None of the participants reported ill health or contraindications to taking part in the study.The study had no time limit.The survey was questionnaire-based and fully anonymous.The description of the research was reviewed by the Bioethics Committee at Poznan University of Medical Sciences (Poland), who issued a statement that the research did not bear the features of a medical experiment and in accordance with the Polish law and GCP was not subject to the opinion of the Bioethics Committee (Statement No. KB-273/22).The Bioethics Committee issues their opinions primary on the basis of the Act of 5 December 1996 on professions of doctor and dentist (including subsequent amendments).In accordance with the recommendations of the Bioethics Committee, the study instructions contained a statement that taking part in the study and handing in the completed questionnaire would be considered as a participant's informed consent to take part in the study.The study was conducted in accordance with the Declaration of Helsinki.The study is part of a large-scale research project on measurement and psychosocial correlates of goal orientation in high performance and recreational athletes with respect to physical activity they undertake.

Statistical analysis
Confirmatory factor analysis was used to assess factor validity.Due to fact that the distribution of the data deviated from a normal distribution, the Satorra-Bentler 36 correction was applied 37,38 .First, the theoretical model of the 3 × 2 AGQ-S was tested.CFI and TLI above 0.90 were assumed to indicate satisfactory values of model fit to the data, and 0.95 and above indicated a very good fit.In contrast, with regard to SRMR and RMSEA, the values below 0.08 were considered satisfactory, while RMSEA values between 0.08 and 0. mediocre fit and above 0.10 were considered a poor fit [39][40][41][42] .Following the authors of the original version of the questionnaire 8 , the fit of alternative models to the data was also verified in order to compare it with the original 3 × 2 model.Alternative models with the following arrangement of factors were tested: (1) a model where the task and self with the same valence were placed on combined factors, and the other-subscales were on their hypothesized factors (2 × 2 model); (2) a model where all items from the task and the self-subscales were placed on one factor, and the other-items on their factors (separate factors for the other-approach and other-avoidance-the trichotomous model); (3) a model where all items from the task and the self-subscales were on one factor, and all items from the other-subscales were on the second factor (the dichotomous model); (4) a model where items from the task-approach and the task-avoidance subscales were on one factor, and all the remaining items were on their factors (Tap/Tav model); (5) a model where items from the self-approach and the self-avoidance subscales were on one factor, and all the remaining items are on their factors (Sap/Sav model); (6) a model where items from the other-approach and the other-avoidance subscales were on one factor, and all the remaining items were on their factors (Oap/Oav model); (7) a model where all items from the approach subscales were placed on one factor, and items from the avoidance subscales were on their factors (approach model); (8) a model where all items from the avoidance subscales were placed on a single factor, and items from the approach subscales were placed on their factors (avoidance model); (9) a model where items that share competence definition were placed on combined factors (three factors: the task, self, other-definition model); (10) a model where two factors were identified based on the valence of approach-avoidance (valence model).
We also analyzed the invariance of measurement with the 3 × 2 AGQ-S scale for the 3 × 2 model among the high-performance and recreational athletes, as well as among men and women.The configural was verified first, followed by the metric (factor loadings in the analyzed groups were fixed), scalar (intercepts in the groups were fixed) and strict (residual values in the groups were fixed).It was assumed that a decrease in CFI values above 0.01 and an increase in RMSEA above 0.015 indicated significant differences between the study groups 43 .
Cronbach's alpha coefficient was used to assess the reliability of the scale.In addition, the quality of subscales and items was assessed by analyzing information curves from the Item Response Theory-the generalized partial credit model.Highly populated information curves were indicative of the large amount of information provided by the measurement of a trait in a specific area and, thus, less measurement error and greater precision of a subscale or item in that area 44,45 .
In addition, as part of investigating validity, a comparison using two-way analysis of variance was made between individuals of different gender and with different levels of sport participation (high-performance, recreational) in terms of the level of achievement goals in sport as measured by the 3 × 2 AGQ-S questionnaire.To assess individual relationships between the personality traits and achievement goals r-Pearson was used.Multiple regression analysis was used to assess the combined contribution of the personality traits to achievement goals in sport.The analysis was performed using R environment and Statistica software (ver.13.3).

Construct validity of the 3 × 2 AGQ-S
Model No. 1 (Fig. 1) estimated in line with the theoretical assumptions of the 3 × 2 achievement goals in sport model, obtained the best (compared to alternative models) and a generally good fit to the data in terms of CFI, TLI, SRMR indexes.Only the RMSEA value was slightly too high.The other models, which were estimated according to other theoretical assumptions, did not provide a good fit to the data (Table 1).
The factor loadings for model 1 (original) are presented in Fig. 1.
The estimated models under invariance analysis fit the data relatively well.The decreases in CFI are less than 0.01 and the RMSEA values do not increase above 0.015 in any case, hence the assumption of measurement invariance in the study groups (women-men, high-performance athletes-recreational athletes) can be taken as confirmed (Table 2).

Information curves for the 3 × 2 AGQ-S questionnaire-The IRT model
The graphs presenting the information curves indicate that, in general, more information was obtained for the scores of low and medium subscales, as well as items of the 3 × 2 AGQ-S questionnaire.In particular, more information for lower trait values was obtained for the task-approach and self-approach subscales.The other subscales and items also contained a lot of information from the area of medium scores, and less from the high scores (Fig. 2).

Relationship between personality traits and achievement goals in sport
Small positive correlations of extraversion with the task-approach, task-avoidance, and other-approach were observed.In addition, there were small positive correlations of conscientiousness with the task-approach, selfapproach and task-avoidance.Emotional stability was weakly positively related with the task-approach.In turn, intellect was weakly positively correlated with the self-approach and other-approach (Table 4).
In line with small correlations, regression analysis showed that personality variables accounted for a small proportion of achievement goals in sport-determination coefficients did not exceed 3%, and the personality traits as predictors demonstrated relatively small regression coefficients (Table 5).
Similarly to when the group was viewed as a whole, the relationships between the personality traits and achievement goals in separate groups (high-performance athletes, recreational athletes, women, men) were relatively small or failed to achieve statistical significance with a p-value at 0.05 (Table 6).

Discussion
In order to study the validity of the 3 × 2 Achievement Goal Questionnaire for Sport, the authors analyzed its factorial validity, and the relationship of the results from the 3 × 2 AGQ-S with athletes' level of sport participation.In terms of factor validity, an overall satisfactory fit of the 3 × 2 model to the empirical data was demonstrated  www.nature.com/scientificreports/based on the CFI, TLI (values above 0.90) and SRMR (nearly 0.06).Nevertheless, the RMSEA value was slightly too high as it was above 0.08, yet below 0.10 (the value considered unacceptable).The fit of the model to the data, however, was poorer than the fit obtained by the authors of the original version of the questionnaire 8 and slightly worse than the fit values obtained among mainly Chinese athletes by Wang et al. 46 , who adapted the questionnaire directly from the classroom environment to sport.In contrast, the fit indexes of the Polish version were mostly better than those of the Brazilian version 47 .The validity of the Polish version of the questionnaire was also confirmed by the best fit of the 3 × 2 model compared to the competing models taking into account the various assumptions described in the Methods Section (e.g., the 2 × 2 model, the trichotomous and dichotomous model).This result was consistent with the findings of the authors of the original version of the scale 8 .High values of internal consistency indexes (Cronbach's alpha) were also obtained.They were mostly similar to the results obtained by the authors of the original version of the scale 8 .In addition, the quality of the subscales and  www.nature.com/scientificreports/items was also assessed by means of analyzing the information curves from the IRT model.In general, the subscales and test items provide more information and, thus, more precise measurement in the lower and middle areas of the traits studied.In particular, the task-approach and self-approach subscales show higher precision for low values and lower precision for medium and high values of the traits.This result was consistent with the previous analysis of information curves for the task subscale from the Polish versions of the POSQ 18 , TEOSQ 48 and GOEM 19 questionnaires.Measurement invariance was also analyzed in groups of men and women, as well as in groups of high-performance and recreational athletes.There were no large differences in the values of model fit indexes to the data for different types of invariance.Therefore, it can be concluded that women use the 3 × 2 AGQ-S in a similar way to men, and high-performance athletes use it similarly to recreational athletes.It was also demonstrated that highperformance athletes were characterized by higher levels of task-approach, task-avoidance, self-approach and self-avoidance than athletes competing at the recreational level.The results for the task subscales are particularly substantiated, as competitive sports are associated with a greater focus on effectiveness and good performance, which is reflected in the content of these subscales.However, the differences (effects) obtained were not large (based on effect size), and the mean values obtained by recreational athletes on these scales were not low either.This may be related to the fact that the study included recreational athletes who engaged in physical activity with rivalry, which in part may share the characteristics of a competitive sport activity.In addition, men obtained higher scores than women on the other-approach scale, which also supports the validity of the tool.This result is consistent with the results obtained for the Polish versions of the GOEM 19 and POSQ 18 scales.Furthermore, this appears to be justified, as it has been emphasized that men are more competitive than women, and are more inclined to display their abilities 49 , which may be related to both evolutionary and social aspects 19 .
Another objective of the study was also to evaluate the relationships between the Big Five personality traits model and the achievement goals from the 3 × 2 model in sport.The observed relationships were small.Hence, despite certain differences depending on the separate groups, the correlations slightly differed.However, it is possible to relate the obtained results to previous research findings in terms of the directions of the obtained correlations.Extraversion, conscientiousness and emotional stability were positively related with the task-approach.In addition, conscientiousness and intellect were also positively related to self-approach.The directions of these relationships were quite consistent with our assumptions and the results presented by McCabe et al. 26 for the 2 × 2 model.The same directions of correlation of the mentioned personality traits with learning orientation (mastery) were obtained by Kaspi-Baruch 50 and Mahlamäki et al. 29 .Additionally, in the case of our participants, extraversion and conscientiousness were positively related with task-avoidance.Due to the smaller number of studies in the presented meta-analysis devoted to the mastery-avoidance factor (divided into task-and self-avoidance in the 3 × 2 model), in this case the comparison of the results is less reliable.However, partially similar relationships were obtained by Chen and Zhang 33 , who showed positive relationships of mastery-avoidance with extraversion, conscientiousness and openness.Additionally, Corker et al. 28 and Asanjarani et al. 51 reported positive correlations between mastery-avoidance and neuroticism.In addition, there was no correlation in our study of agreeableness and intellect with the task-approach, as well as no correlations of emotional stability, extraversion and agreeableness with the self-approach, which is not in line with our assumptions.Yet, there were sometimes similar results, e.g.Wang and Erdheim 22 did not show significant relationships of agreeableness, openness and neuroticism with the mastery (learning) factor, and Hendriks and Payne 52 did not obtain significant correlations of the learning orientation (mastery) factor with agreeableness and neuroticism.On another note, maybe the obtained results Table 6.Relationships between personality traits and achievement goals in sport in groups of highperformance and recreational athletes, and in groups of women and men.Subscales from the 3 × 2 AGQ-S model: Tap task-approach; Tav task-avoidance; Sap self-approach; Sav self-avoidance; Oap other-approach; Oav other-avoidance.The Big Five personality traits (IPIP-BFM- www.nature.com/scientificreports/stem partly from the fact that the 3 × 2 model splits the mastery factor into two components (task and self) and/or that the present study was performed in a sport context as opposed to the studies presented in the meta-analysis, which were conducted primarily in school and work environments.In addition, in our research extraversion and intellect were poorly and positively correlated with the other-approach, although such relationships were not predicted.In contrast, the predicted relationships of conscientiousness, emotional stability and agreeableness with other-approach were not obtained, although in earlier studies these relationships had occurred, yet they had not been strong 32 .Moreover, in our study, the personality traits were not associated with the other-avoidance factor, even though such relationships were to be expected for nearly all traits from the Big Five model.These avenues will require further research devoted to the relations to the 3 × 2 achievement goal model in sport.In the regression models, our study showed that the personality traits accounted for only a small percentage of the variance (not more than 3%) of achievement goals from the 3 × 2 model in sport.In the light of the discussion regarding to what extent personality is a similar construct to goal orientation/achievements 20,53,54 , the low correlations obtained in our study between these variables support the assumption that the mentioned constructs are rather not redundant.It is even possible that the relationships between the personality traits and goals in sport are mediated by other variables.On another note, maybe achievement goals in sport may rather stem from a favorable developmental context, such as an appropriate motivational setting in the sports environment 55 than the personality traits themselves.Another factor contributing to lower correlations in groups of athletes may also be their selection in view of certain personality traits.In addition, we also analyzed the relationships between the personality traits and achievement goals in groups of men and women, as well as among high-performance and recreational athletes.Nonetheless, these relationships were also relatively weak, generally not exceeding 0.20, and they did not differ considerably across the groups.This issue requires further research.The present study is not free from limitations.The study was conducted on relatively young people; it is therefore worth extending the study to athletes of different ages.Performing validation on one group of athletes is also a certain limitation, hence it is worth verifying the validity of the construct on other groups of professional and recreational athletes.In further research and analysis of the Polish version of the 3 × 2 AGQ-S questionnaire it is also worthwhile to compare team and individual athletes with regard to achievement goals (the 3 × 2 model).Moreover, it is vital to expand the study with the testing of convergent validity, so as to evaluate the relationships of the scale with other tools measuring similar constructs.In addition, it is worth extending the validation study to include relations of the 3 × 2 AGQ-S with tools to measure other constructs that are theoretically important from the perspective of the questionnaire under investigation.It is essential to present various measures of the criterion validity of the scale by assessing the relationships of achievement goals in sport with such factors as sport performance.It is also worth analyzing the reliability of the scale using the test-retest method.
In conclusion, the conducted study demonstrates that the Polish version of the 3 × 2 AGQ-S questionnaire shows satisfactory indicators of validity and reliability.It can therefore be used both in scientific research in sport and in the field of sport practice.A significant aspect of this contribution was the extension of validation to high-performance and recreational athletes.In the analysis of measurement invariance, it was demonstrated that individual groups use the 3 × 2 AGQ-S questionnaire in a similar manner.Furthermore, women use the scale similarly to men.Relationships between the Big Five personality traits model and the achievement goals from the 3 × 2 model in sport were also presented.The obtained correlations, however, were not very strong, indicating the need for further investigations into the psychosocial determinants of achievement goals in sport.

Figure 2 .
Figure 2. Information curves for subscales (thick line) and items of the 3 × 2 AGQ-S questionnaire.

Table 1 .
Fitting the original 3 × 2 achievement goal model (Model 1) and alternative models to the data.

Table 2 .
Measurement invariance of the 3 × 2 AGQ-S scale by gender and level of sport participation.

Table 3 .
Level of achievement goals in groups of high-performance and recreational athletes, and in groups of women and men.Subscales from the 3 × 2 AGQ-S model: Tap task-approach; Tav task-avoidance; Sap selfapproach; Sav self-avoidance; Oap other-approach; Oav other-avoidance.HP high-performance athletes; R recreational athletes; F female; M male.

Table 4 .
Relationships between personality traits and achievement goals in sport for the whole group.